Robustness in Consensus Networks

TL;DR

This paper develops a formal framework to analyze the robustness of large consensus networks, establishing tight bounds on how performance measures scale with network size and topology.

Contribution

It provides the first tight bounds linking robustness and convergence speed in consensus networks, independent of network topology.

Findings

Tight bounds on convergence speed related to robustness.

Performance measures scale predictably with network size.

Results applicable across various network topologies.

Abstract

We consider the problem of robustness in large consensus networks that occur in many areas such as distributed optimization. Robustness, in this context, is the scaling of performance measures, e.g. H2-norm, as a function of network dimension. We provide a formal framework to quantify the relation between such performance scaling and the convergence speed of the network. Specifically, we provide upper and lower bounds for the convergence speed in terms of robustness and discuss how these bounds scale with the network topology. The main contribution of this work is that we obtain tight bounds, that hold regardless of network topology. The work here also encompasses some results in convergence time analysis in previous literature.